MathsAges 16-18

2×2 matrix determinants

Evaluate the determinant det(M) = ad − bc of a 2 × 2 matrix from its leading and secondary diagonals. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

2×2 matrix determinants

Take your time. Show your thinking.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [7, 11]].
M = [ 11 6 ; 7 11 ] · det(M) = (11×11) − (6×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [9, 12]].
M = [ 6 1 ; 9 12 ] · det(M) = (6×12) − (1×9)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [6, 7]].
M = [ 11 2 ; 6 7 ] · det(M) = (11×7) − (2×6)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 11]].
M = [ 4 2 ; 9 11 ] · det(M) = (4×11) − (2×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 7]].
M = [ 7 9 ; 9 7 ] · det(M) = (7×7) − (9×9)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 8]].
M = [ 2 3 ; 2 8 ] · det(M) = (2×8) − (3×2)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [4, 7]].
M = [ 6 2 ; 4 7 ] · det(M) = (6×7) − (2×4)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 7]].
M = [ 8 7 ; 8 7 ] · det(M) = (8×7) − (7×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 11]].
M = [ 8 3 ; 5 11 ] · det(M) = (8×11) − (3×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [2, 2]].
M = [ 9 8 ; 2 2 ] · det(M) = (9×2) − (8×2)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [9, 4]].
M = [ 5 2 ; 9 4 ] · det(M) = (5×4) − (2×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [1, 3]].
M = [ 9 8 ; 1 3 ] · det(M) = (9×3) − (8×1)

12 questions · Seed 104730 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

2×2 matrix determinants

Answers and reasoning. Review before teaching.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [7, 11]].
79
det(M) = (11 × 11) − (6 × 7) = 121 − 42 = 79.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [9, 12]].
63
det(M) = (6 × 12) − (1 × 9) = 72 − 9 = 63.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [6, 7]].
65
det(M) = (11 × 7) − (2 × 6) = 77 − 12 = 65.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 11]].
26
det(M) = (4 × 11) − (2 × 9) = 44 − 18 = 26.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 7]].
-32
det(M) = (7 × 7) − (9 × 9) = 49 − 81 = -32.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 8]].
10
det(M) = (2 × 8) − (3 × 2) = 16 − 6 = 10.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [4, 7]].
34
det(M) = (6 × 7) − (2 × 4) = 42 − 8 = 34.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 7]].
0
det(M) = (8 × 7) − (7 × 8) = 56 − 56 = 0.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 11]].
73
det(M) = (8 × 11) − (3 × 5) = 88 − 15 = 73.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [2, 2]].
2
det(M) = (9 × 2) − (8 × 2) = 18 − 16 = 2.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [9, 4]].
2
det(M) = (5 × 4) − (2 × 9) = 20 − 18 = 2.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [1, 3]].
19
det(M) = (9 × 3) − (8 × 1) = 27 − 8 = 19.

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

2×2 matrix determinants

Take your time. Show your thinking.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [7, 11]].
M = [ 11 6 ; 7 11 ] · det(M) = (11×11) − (6×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [9, 12]].
M = [ 6 1 ; 9 12 ] · det(M) = (6×12) − (1×9)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [6, 7]].
M = [ 11 2 ; 6 7 ] · det(M) = (11×7) − (2×6)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 11]].
M = [ 4 2 ; 9 11 ] · det(M) = (4×11) − (2×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 7]].
M = [ 7 9 ; 9 7 ] · det(M) = (7×7) − (9×9)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 8]].
M = [ 2 3 ; 2 8 ] · det(M) = (2×8) − (3×2)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [4, 7]].
M = [ 6 2 ; 4 7 ] · det(M) = (6×7) − (2×4)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 7]].
M = [ 8 7 ; 8 7 ] · det(M) = (8×7) − (7×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 11]].
M = [ 8 3 ; 5 11 ] · det(M) = (8×11) − (3×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [2, 2]].
M = [ 9 8 ; 2 2 ] · det(M) = (9×2) − (8×2)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [9, 4]].
M = [ 5 2 ; 9 4 ] · det(M) = (5×4) − (2×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [1, 3]].
M = [ 9 8 ; 1 3 ] · det(M) = (9×3) − (8×1)

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

2×2 matrix determinants

Answers and reasoning. Review before teaching.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [7, 11]].
79
det(M) = (11 × 11) − (6 × 7) = 121 − 42 = 79.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [9, 12]].
63
det(M) = (6 × 12) − (1 × 9) = 72 − 9 = 63.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [6, 7]].
65
det(M) = (11 × 7) − (2 × 6) = 77 − 12 = 65.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 2], [9, 11]].
26
det(M) = (4 × 11) − (2 × 9) = 44 − 18 = 26.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [9, 7]].
-32
det(M) = (7 × 7) − (9 × 9) = 49 − 81 = -32.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 8]].
10
det(M) = (2 × 8) − (3 × 2) = 16 − 6 = 10.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [4, 7]].
34
det(M) = (6 × 7) − (2 × 4) = 42 − 8 = 34.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 7]].
0
det(M) = (8 × 7) − (7 × 8) = 56 − 56 = 0.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 11]].
73
det(M) = (8 × 11) − (3 × 5) = 88 − 15 = 73.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [2, 2]].
2
det(M) = (9 × 2) − (8 × 2) = 18 − 16 = 2.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 2], [9, 4]].
2
det(M) = (5 × 4) − (2 × 9) = 20 − 18 = 2.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [1, 3]].
19
det(M) = (9 × 3) − (8 × 1) = 27 − 8 = 19.

12 questions · Seed 104730 · Age guidance, not curriculum certification